Properties

Label 1344.1.bn
Level $1344$
Weight $1$
Character orbit 1344.bn
Rep. character $\chi_{1344}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $2$
Sturm bound $256$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1344.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1344, [\chi])\).

Total New Old
Modular forms 68 12 56
Cusp forms 20 4 16
Eisenstein series 48 8 40

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{9} + 4q^{13} - 4q^{21} - 2q^{25} - 2q^{37} - 2q^{49} - 4q^{57} + 4q^{61} + 2q^{73} - 2q^{81} - 2q^{93} + 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1344.1.bn.a \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.1.bn.b \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)